The Palestinian group is believed to be planning to accept a deal for a year-long ceasefire to start this Thursday that would replace the fragile truce both sides declared after a three-week Israeli offensive aimed at halting the rocket fire.

Egypt, meanwhile, which is brokering the ceasefire talks, awaits official word on what Hamas has decided.

In the interim, Mr. Olmert, under pressure for a strong reaction to sporadic rocket attacks, told his Cabinet, "If there will be firing on residents of the south, there will be a strong Israeli reaction that will be disproportionate."

"We will act according to new rules that ensure we will not be dragged into an incessant shoot-out that prevents us from living normal lives in the south," he said.

Hamas has denied firing rockets and it is smaller splinter groups that are considered to be responsible for them.

Olmert's comments were made on a day four rockets were fired across the border from Gaza into Israel and an Israeli army patrol was fired upon along the border fence. There were no injuries in any of the incidents but one of the rockets fell near a nursery school in the western Negev Desert.

The ceasefire between the sides has been a shaky one from the start. Last week an Israeli officer was killed by a roadside bomb while patrolling the border fence with Gaza and Israel has responded to this and other attacks with air strikes.

Olmert's call for a harsher response comes ahead of next week's parliamentary elections in Israel.

Foreign Minister Tzipi Livni who played a key role in the operation on Gaza is running as the head of the ruling Kadima party where she continues to slip in the polls against her main rival, Benjamin Netanyahu of the right-wing Likud Party.

Mr. Netanyahu is running as a hardliner and his campaign has belittled Miss. Livni's security credentials.

The growing feeling in Israel is that the Gaza operation ended with uncertain results despite the devastating use of firepower used. Miss Livni and other government leaders had promised it would lead to a new reality on the ground, something the continued rocket-fire seems to dispute.

Nearly 1,300 Palestinians, over half of them civilians were killed in the fighting according to officials in Gaza. On the Israeli side ten soldiers and three civilians were killed.

Hamas' ability to continue smuggling in weapons, including longer-range rockets across the Egyptian border into Gaza – often through underground tunnels – has been one of Israel's main concerns.

The Al-Arabiya report said Hamas had agreed to let the Palestinian Authority President Mahmoud Abbas of the rival Fatah party oversee Gaza's border crossings as part of a peace deal, something Israel has agreed to in the past.